Simplify the Radical Expression 8 square root of 32x

$8 \sqrt{32 x}$

Step 1

Rewrite $32 x$ as ${(2^{2})}^{2} \cdot (2 x)$ .

Factor $16$ out of $32$ .

$8 \sqrt{16 (2) x}$

Rewrite $16$ as $4^{2}$ .

$8 \sqrt{4^{2} \cdot 2 x}$

Rewrite $4$ as $2^{2}$ .

$8 \sqrt{{(2^{2})}^{2} \cdot 2 x}$

Add parentheses.

$8 \sqrt{{(2^{2})}^{2} \cdot (2 x)}$

Step 2

Pull terms out from under the radical.

$8 (| 2^{2} | \sqrt{2 x})$

Step 3

Raise $2$ to the power of $2$ .

$8 (| 4 | \sqrt{2 x})$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$8 (4 \sqrt{2 x})$

Step 5

Multiply $4$ by $8$ .

$32 \sqrt{2 x}$